Setting out of perpendiculars at various points on given line

Setting out of perpendiculars at various points on given line
  • Author: Farhan Khan
  • Posted On: April 24, 2021
  • Updated On: April 24, 2021


The primary aim of this survey job is to set out perpendiculars at various points on a given line.


  • Cross staff
  • Optical square
  • Arrows
  • Chain
  • Fiber glass tape
  • Ranging rods

Least count of the instrument:

Least count of fiber glass tape = 0.01 m

Least count of metric chain = 0.02 m


Perpendiculars can be drawn from the survey line using various instruments and methods. Following are some of the instruments and procedures that are useful in setting out perpendiculars from a given survey line at various points in the field.

1)Procedure to set up a perpendicular by cross-staff:

The procedure to set out a perpendicular on a given chain line with cross-staff is as follows:

  • Hold the cross-staff vertically at the approximate position.
  • Assume, slits A and B are directed towards the ranging rods R and R1 that are fixed at the end stations.
  • Direct slits C and D towards the object O.
  • Bisect the ranging rods by looking through the slits A and B.
  • Bisect the object O by looking through slits C and D at the same time.
  • Move the staff forward or backward along the chain line to bisect the object and the raging rods simultaneously.


The cross-staff is a simple instrument available that is suitable for setting out right angles on a survey line. It has three types:

  1. Open cross-staff
  2. French cross-staff
  3. Adjustable cross-staff

The most commonly use out of these is the open cross-staff.

Open cross-staff

The open cross-staff comprises of four metal arms having vertical splits in them. These two pairs of arms AB and BC are perpendicular to each other. The purpose of vertical slits is to sight the object and the ranging rods.

The cross-staff is mounted on a wooden pole of 2.5 cm diameter and 1.5 m in length. The end of the pole is fitted with an iron shoe to help provide grip when it is placed on the ground surface.

Open cross-staff

French cross-staff

This instrument has an octagonal shape and comprises of an octagonal brass tube having slits on all its eight sides. It contains an alternate vertical sighting slit and opposite vertical window along with a fine vertical wire or horsehair on each of the four sides that are used for setting out perpendiculars.

It also has vertical slits on the other sides for setting out angles of 45 degrees. It contains a socket at the base to help it mount on the pointed staff while using it in the field. French cross-staff is not as accurate as cross-staff.

Adjustable cross-staff

It comprises of a brass cylindrical tube that is 1 cm deep and 8 cm in diameter. It is divided in the center. The upper cylindrical part can be rotated relative to the lower part employing a circular rack and pinion arrangement actuated by a screw.

Both cylindrical parts have sighting slits; the lower part has graduations in degrees and sub-divisions while the upper part carries a Vernier scale. Thus, it can set outlines of any desired angle. It also has a magnetic compass at the top to observe the bearings of the survey lines.

2)Procedure to set up a perpendicular by optical square:

The procedure to set out a perpendicular with an optical square is as follows:

  • Firstly, the observer should stand on the chain line and roughly at that point where the perpendicular is required to be set up.
  • Hold the optical square by arm at eye level.
  • Observe the ranging rod at the forward station B through the unpolished portion on the lower part of the horizon glass.
  • Sight the image of the object P by looking through the upper silvered portion of the horizon glass.
  • If the ranging rod B and the image of the object P do not coincide, then move forward or backward along the chain line until the ranging rod B and the image of the object P exactly coincide.
  • Mark this position on the ground to locate the foot of the perpendicular.

Optical square

Another instrument to set out perpendiculars on a survey line is the optical square. It consists of a small circular metal box having a diameter of 5 cm and a depth of 1.25 cm. It also has a metal cover to slide around the box and cover the slits. Optical square works according to the principle of reflecting surfaces.

The angle of incidence between the first ray and the last reflected ray is twice the angle between the mirrors. The angle between the mirrors is fixed at 45 degrees in this case. Hence, the angle between the horizon sight and index sight will become 90 degrees.

Optical square

3)Procedure to set out a perpendicular by prismatic square:

Hold the prismatic square in your hand and see directly over the prism to sight the ranging rod at B.

Walk along the chain line until the image of the object O and the prism coincide with the ranging rod at B.

Prismatic square

Prismatic square is a modern and reliable method for setting out perpendicular on a given survey line. It is based on the same working principle as the optical square. Prismatic square is brighter than optical square and it requires no adjustment because the angle between the prism and reflecting surface is fixed to 45 degrees. It is not affected by dust and can be conveniently used in dim light.

4)Procedure to set out a perpendicular by 3-4-5 method

Let AB be the chain line and a perpendicular is required to be set up at point C of this line. Establish a point D at 3 meters distance. 5 meters and 6 meters marks are brought together to form a loop. The tape is stretched tight by fastening the ends D and C. the point D is established such that:

DE2 = CD2 + DE2

52 = 32 + 42 = 25

Thus, angle DCE = 90 degrees

CE is perpendicular to the chain line at C.

Procedure to set out a perpendicular by 3-4-5 method

Results & Discussions:

The perpendiculars on the given survey line have been successfully set out by adopting any of the above-described instruments and procedures.


  • Helmet, protective shoes, and reflective vests must be worn by all field workers.
  • Handle all instruments with caution.
  • Follow the proper step-by-step procedure to avoid any errors.
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Author: Farhan Khan

Farhan is a highly experienced civil engineer from the Southern side of Texas and has been associated with ConstructionHow since 2020. Over almost a decade, his wide span of expertise enabled him to bring forth his fair share of stories and experiences related to the most iconic engineering examples worldwide. He has also contributed to online and offline publications on requests. Engineering is his passion, which is why he chose to become part of our honorable team of industry experts looking to provide authentic and credible guidelines to the reader.